Green began riding at the age of four and is most well known for winning the Badminton Horse Trials a record six times, on six different horses: Be Fair (1973), Wideawake (1976), George (1977), Killaire (1979), Regal Realm (1983) and Beagle Bay (1984). In addition, she was placed second on Village Gossip (1978). She has also won the Tony Collins Trophy, awarded to the British rider with the greatest number of points in eventing in a season, a record seven times.

Green first represented Britain at the 1973 European Championships at Kiev. She competed in the European Championships a total of seven times and was European Champion in 1975, on Be Fair, and again in 1977, on George.

She attended her first Olympics in 1976, at the Montreal Games. However, she had to retire after the cross-country event after her mount, Be Fair, slipped a tendon on course. In 1980, the British Equestrian Team took part in the 1980 Summer Olympics boycott, and Green represented Great Britain at the alternative Olympics at Fontainebleau, where she was in 69th place after the dressage, rising to 7th after the cross-country ride, on Village Gossip.

In 1982, she went on to represent Britain at the Eventing World Championships in Luhmühlen, where she won the individual gold medal on Regal Realm, as well as being part of the gold medal winning team. She was part of the silver medal winning British Team at the 1983 European Eventing Championships in Switzerland, where she also won an individual silver medal.

In 1984, Green attended Badminton, and not only won for the sixth time, on Beagle Bay, but also placed fifth on Village Gossip. Later that year, at the Los Angeles Olympics, she represented the silver medal British Team and individually placed 6th.

Green became a mother in 1985, and she retired for a few months before returning to international competition later that year and helping the British Team win the gold at the European Championships held at Burghley. She was short-listed to attend the 1986 World Championships as well, but an injury to her horse forced her to withdraw. However, in late 1986 she went on to win the event at Boekelo.

Green finished her international career after attending the 1987 European Championships in Luhmuhlen. She now is a commentator for major events, and conducts clinics worldwide. Green is a member of the Board of Directors of British Eventing, formerly the British Horse Trials Association and a team selector

Red Mile Entertainment released the video game "Lucinda Green's Equestrian Challenge" for the PlayStation 2 game console on 16 November 2006.